What is the derivative of y=6log_{5}(x^2-6) ?

The derivative of y=6log_{5}(x^2-6) is (12x)/(ln(5)(x^2-6))

What is the first derivative of y=6log_{5}(x^2-6) ?

The first derivative of y=6log_{5}(x^2-6) is (12x)/(ln(5)(x^2-6))

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derivative of

y = 6 lo g_{5} (x^{2} - 6)

\frac{12 x}{ln ( 5 ) ( x ^{2} - 6 )}

Solution steps

\frac{d}{d x} (6 lo g_{5} (x^{2} - 6))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (lo g_{5} (x^{2} - 6))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= 6 \frac{d}{d x} (\frac{ln ( x ^{2} - 6 )}{ln ( 5 )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \cdot \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (x^{2} - 6))

Apply the chain rule:

\frac{1}{x ^{2} - 6} \frac{d}{d x} (x^{2} - 6)

= \frac{1}{x ^{2} - 6} \frac{d}{d x} (x^{2} - 6)

\frac{d}{d x} (x^{2} - 6) = 2 x

= 6 \cdot \frac{1}{ln ( 5 )} \cdot \frac{1}{x ^{2} - 6} \cdot 2 x

Simplify

6 \cdot \frac{1}{ln ( 5 )} \cdot \frac{1}{x ^{2} - 6} \cdot 2 x : \frac{12 x}{ln ( 5 ) ( x ^{2} - 6 )}

= \frac{12 x}{ln ( 5 ) ( x ^{2} - 6 )}

y = (5 - 2 x^{3})^{3}

\int 2^{x} x^{2} d x

\int x^{5} x^{6} + 3 d x

f (x) = \frac{e ^{x}}{- 8 x ^{7}}

y^{^{'}} + y = t e^{- t} + e^{t}

What is the derivative of y=6log_{5}(x^2-6) ?
The derivative of y=6log_{5}(x^2-6) is (12x)/(ln(5)(x^2-6))
What is the first derivative of y=6log_{5}(x^2-6) ?
The first derivative of y=6log_{5}(x^2-6) is (12x)/(ln(5)(x^2-6))